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Simplifying Non-Perfect Squares

Simplifying Non-Perfect Squares. What is a square root?. Two identical factors of a number. What if it is a Non-Perfect Square???? How do you find the two identical factors? There are two methods to consider. 5 and 5. Method #1 – Estimating.

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Simplifying Non-Perfect Squares

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  1. Simplifying Non-Perfect Squares

  2. What is a square root? • Two identical factors of a number. • What if it is a Non-Perfect Square???? • How do you find the two identical factors? • There are two methods to consider. 5 and 5

  3. Method #1 – Estimating • Find the square root to one decimal place. This is an approximation. • Find the square root of 20 up to one decimal place. • What two perfect squares does 20 lie between? It lies between 16 and 25. • We know the square root of 16 is 4. So the square root of 20 must be a little more than 4.

  4. Method #1 – Estimating continued… • Here’s how to find that “little more.” • Think of how far 20 is between 16 and 25. Is it closer to one or the other? • 20 seems to be in the middle. So try 4.5(4.5). • You get 20.25. • That is pretty close to 20. • This means that the square root of 20 is about 4.5.

  5. Method #2 - Rationalizing • We are going to “simplify” the radical (square root #) as much as possible. • Find the square root of 20. • Think about what “PERFECT SQUARES” are factors of 20. • The only perfect square factor is 4. • 4 times 5 equals 20.

  6. Method #2 – Rationalizing continued… • What is the square root of 4? • 2 • We can simplify the square root of 20 to

  7. Prove that this is true… 2 • 2 = 4 4 • 5 = 20

  8. Find the • This is not a perfect square. • Think of all the perfect square factors: • 16 times 3 • 4 times 12 (12 is really 4 times 3) • The BEST perfect square factor is 16.

  9. Find the • This is not a perfect square. • Think of all the perfect square factors: • 100 times 2 • 25 times 8 (8 is really 4 times 2) • The BEST perfect square factor is 100.

  10. Rationalize the following:

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